Question

1. which data set indicates the strongest linear relationship between its two variables?
2. which data set has an apparent negative, but not perfect, linear relationship between its two variables?
3. for which data set does the correlation coefficient r appear to be equal to - 1?

Explanation:

Step1: Recall linear - relationship concept

The closer the data points are to a straight - line, the stronger the linear relationship.

Step2: Analyze Figure 1

Data points in Figure 1 are scattered randomly, indicating a weak or no linear relationship.

Step3: Analyze Figure 2

Data points in Figure 2 are closely clustered around an upward - sloping line, showing a strong positive linear relationship.

Step4: Analyze Figure 3

Data points in Figure 3 are closely clustered around a downward - sloping line, showing a strong negative linear relationship.

Step5: Analyze Figure 4

Data points in Figure 4 form a curved pattern, so there is no linear relationship.

1. For the question "Which data set indicates the strongest linear relationship between its two variables?", the answer is Figure 2 or Figure 3 as they both have data points closely clustered around a straight line. But usually, when we consider the concept of "strongest" without further context, we can say Figure 2 (since the points seem to be even more closely grouped).
2. For the question "Which data set has an apparent negative, but not perfect, linear relationship between its two variables?", the answer is Figure 3. The points follow a downward - sloping trend but are not exactly on a single straight line.
3. For the question "For which data set does the correlation coefficient r appear to be equal to - 1?", a correlation coefficient of r=-1 indicates a perfect negative linear relationship. None of the given figures show a perfect negative linear relationship (where all points lie exactly on a straight line), but Figure 3 has the closest negative linear trend among them.

Answer:

1. Figure 2
2. Figure 3
3. None of the figures (but if we have to choose the closest, Figure 3)